Glass-based articles with sections of different thicknesses

ABSTRACT

Glass-based articles having sections of different thicknesses where a maximum central tension in a thinner section is less than that of a thicker section. The articles comprise an alkali metal oxide having a independent nonzero concentrations that vary along at least a portion of the thickness of each section. Consumer electronic products may comprise the glass-based articles having sections of different thicknesses.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application and claims the benefit ofpriority of U.S. application Ser. No. 16/150,816 filed on Oct. 3, 2018,which in turn, claims the benefit of priority of U.S. ProvisionalApplication Ser. No. 62/570,344 filed on Oct. 10, 2017, the contents ofeach of which are relied upon and incorporated herein by reference intheir entireties.

FIELD

Embodiments of the disclosure generally relate to glass-based articleshaving sections of different thicknesses and methods for manufacturingthe same.

BACKGROUND

Glass-based articles are used in many various industries includingconsumer electronics, transportation, architecture, defense, medical,and packaging. For consumer electronics, glass-based articles are usedin electronic devices as cover plates or windows for portable or mobileelectronic communication and entertainment devices, such as mobilephones, smart phones, tablets, video players, information terminal (IT)devices, laptop computers, navigation systems and the like. Inarchitecture, glass-based articles are included in windows, showerpanels, and countertops; and in transportation, glass-based articles arepresent in automobiles, trains, aircraft, and sea-craft. Glass-basedarticles are suitable for any application that requires superiorfracture resistance but thin and light-weight articles. For eachindustry, mechanical and/or chemical reliability of the glass-basedarticles is typically driven by functionality, performance, and cost.Improving the mechanical and/or chemical reliability of these articlesis an ongoing goal.

Chemical treatment is a strengthening method to impart adesired/engineered stress profile having one or more of the followingparameters: compressive stress (CS), depth of compression (DOC), andmaximum central tension (CT). Many glass-based articles, including thosewith engineered stress profiles, have a compressive stress that ishighest or at a peak at the glass surface and reduces from a peak valuemoving away from the surface, and there is zero stress at some interiorlocation of the glass article before the stress in the glass articlebecomes tensile. Chemical strengthening by ion exchange (IOX) ofalkali-containing glass is a proven methodology in this field.

In the consumer electronics industry, chemically-strengthened glass isused as a preferred material for display covers due to better aestheticsand scratch resistance compared to plastics, and better drop performanceplus better scratch resistance compared to non-strengthened glass. Inthe past, thickness of cover glass has been mostly uniform (except nearthe edges). But recently, there has been interest in cover glass designsof non-uniform thicknesses away from the edges.

There is a need for chemically-strengthened glass articles havingnon-uniform thicknesses.

SUMMARY

Aspects of the disclosure pertain to glass-based articles havingsections of different thicknesses and methods for their manufacture.

According to aspect (1), a glass-based article is provided. Theglass-based articles comprising: a first section having a firstthickness (t₁) and a first section surface; a second section having asecond thickness (t₂), and a second section surface, wherein t₂ is lessthan t₁, a first stress profile of the first section comprising: a firstcompressive stress region; and a first central tension region comprisinga first maximum central tension (CT₁); a second stress profile of thesecond section comprising: a second compressive stress region; and asecond central tension region comprising a second maximum centraltension (CT₂); and an alkali metal oxide having a first non-zeroconcentration that varies in the first section from the first sectionsurface into at least a portion of t₁ and a second non-zeroconcentration that varies in the second section from the second sectionsurface into at least a portion of t₂; wherein CT₂ is less than CT₁.

According to aspect (2), the glass-based article of aspect (1) isprovided, including a soda-lime silicate, an alkali-aluminosilicate, analkali-containing borosilicate, an alkali-containingaluminoborosilicate, or an alkali-containing phosphosilicate.

According to aspect (3), the glass-based article of aspect (2) isprovided, including a lithium-containing aluminosilicate.

According to aspect (4), the glass-based article of any one of aspects(1) to (3) is provided, wherein the second section is off-set from alledges of the glass-based article.

According to aspect (5), the glass-based article of any one of aspects(1) to (4) is provided, wherein t₂ is less than t₁ by at least 100microns.

According to aspect (6), the glass-based article of any one of aspects(1) to (5) is provided, wherein t₂ is in the range of 0.05·t₁ to0.96·t₁.

According to aspect (7), the glass-based article of any one of aspects(1) to (6) is provided, wherein t₁ is in the range of 0.3 mm to 2.5 mm,and t₂ is in the range of 0.025 mm to 2.4 mm.

According to aspect (8), the glass-based article of any one of aspects(1) to (7) is provided, wherein the first stress profile furthercomprises a first depth of compression (DOC₁) that is located at 0.15·t₁or deeper.

According to aspect (9), the glass-based article of aspect (8) isprovided, wherein DOC₁ is in the range of 0.15·t₁ to 0.23·t₁.

According to aspect (10), the glass-based article of any one of aspects(1) to (9) is provided, wherein the second stress profile furthercomprises a second depth of compression (DOC₂) that is located at0.075·t₂ or deeper.

According to aspect (11), the glass-based article of aspect (10) isprovided, wherein DOC₂ is in the range of 0.075·t₂ to 0.15·t₂.

According to aspect (12), the glass-based article of any one of aspects(1) to (11) is provided, wherein the first stress profile furthercomprises a first surface compressive stress (CS₁) in the firstcompressive stress region of 450 MPa or more; and the second stressprofile further comprises a second surface compressive stress (CS₂) inthe second compressive stress region of 450 MPa or more.

According to aspect (13), the glass-based article of any one of aspects(1) to (12) is provided, wherein a portion of the first stress profileextends from the first section surface to a knee, wherein the knee islocated at a depth from the first section surface in the range of about2 to about 30 micrometers, and all points of the first stress profilelocated between the first section surface and the knee comprise atangent having a value that is 10 MPa/micrometer or greater.

According to aspect (14), the glass-based article of aspect (13) isprovided, wherein a portion of the first stress profile extends from theknee to a first depth of compression (DOC₁), wherein all points of thefirst stress profile located between the knee and DOC₁ comprise atangent having a value that is between about 0 and 2 MPa/micrometer.

According to aspect (15), the glass-based article of any one of aspects(1) to (14) is provided, wherein the alkali metal oxide comprises one ormore of: lithium, potassium, and sodium.

According to aspect (16), the glass-based article of any one of aspects(1) to (15) is provided, further comprising one or more metals selectedfrom the group consisting of: silver, copper, zinc, titanium, rubidium,and cesium.

According to aspect (17), a consumer electronic product is provided. Theconsumer electronic product comprising: a housing having a frontsurface, a back surface, and side surfaces; electrical componentsprovided at least partially within the housing, the electricalcomponents including at least a controller, a memory, and a display, thedisplay being provided at or adjacent the front surface of the housing;and a cover plate disposed over the display; wherein a portion of atleast one of the housing and the cover plate comprises the glass-basedarticle of one of aspects (1) to (16).

According to aspect (18), a method of manufacturing a glass-basedarticle is provided. The method comprising: exposing a first sectionhaving a first thickness (t₁) and a first section surface and a secondsection having a second thickness (t₂) and a second section surface of aglass-based substrate to a bath comprising alkali metal ions toion-exchange the glass-based substrate and form the glass-based articlecomprising an alkali metal oxide having a first non-zero concentrationthat varies in the first section from the first section surface into atleast a portion of t₁ and a second non-zero concentration that varies inthe second section from the second section surface into at least aportion of t₂; wherein t₂ is less than t₁, and the glass-based articlehas a first stress profile of the first section comprising a firstcentral tension region comprising a first maximum central tension (CT₁)and a second stress profile of the second section comprising a secondcentral tension region comprising a second maximum central tension(CT₂), wherein CT₂ is less than CT₁.

According to aspect (19), the method of aspect (18) is provided, whereinthe glass-based substrate is exposed to a first bath comprising alkalimetal ions for a first duration, and subsequently to a second bathcomprising alkali metal ions for a second duration.

According to aspect (20), the method of aspect (18) is provided, whereinthe glass-based substrate is a lithium-containing aluminosilicate andthe bath comprises ions of potassium and sodium.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, which are incorporated in and constitute apart of this specification, illustrate several embodiments describedbelow.

FIG. 1 illustrates an exemplary glass-based article;

FIG. 2 illustrates a pocket of an article;

FIG. 3 illustrates a cross-section of the pocket of FIG. 2 ;

FIG. 4A illustrates a cross-section of the article of FIG. 1 ;

FIG. 4B illustrates a close-up cross-section of a portion of the articleof FIG. 1 with a different thickness;

FIG. 5A is a plan view of an exemplary electronic device incorporatingany of the strengthened laminated glass-based articles disclosed herein;

FIG. 5B is a perspective view of the exemplary electronic device of FIG.5A;

FIG. 6 is a graph of three parameters: compressive stress (CS), centraltension (CT), and depth of compression (DOC) as a function of scaleddiffusion distance;

FIG. 7 is a graph of scaled concentration versus normalized position;

FIG. 8 is a graph of stress versus normalized position;

FIG. 9 is a graph of stress versus absolute position for Example 1 andComparative Example A;

FIG. 10 is a graph of stress versus normalized position for Example 1and Comparative Example A; and

FIG. 11 is the graph of FIG. 10 enlarged to the center (0.5 t) position.

DETAILED DESCRIPTION

Before describing several exemplary embodiments, it is to be understoodthat the disclosure is not limited to the details of construction orprocess steps set forth in the following disclosure. The disclosureprovided herein is capable of other embodiments and of being practicedor being carried out in various ways.

Reference throughout this specification to “one embodiment,” “certainembodiments,” “various embodiments,” “one or more embodiments” or “anembodiment” means that a particular feature, structure, material, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the disclosure. Thus, the appearances ofthe phrases such as “in one or more embodiments,” “in certainembodiments,” “in various embodiments,” “in one embodiment” or “in anembodiment” in various places throughout this specification are notnecessarily referring to the same embodiment. Furthermore, theparticular features, structures, materials, or characteristics may becombined in any suitable manner in one or more embodiments.

The terms “glass-based article” and “glass-based substrates” are used toinclude any object made wholly or partly of glass, includingglass-ceramics (including an amorphous phase and a crystalline phase).Laminated glass-based articles include laminates of glass and non-glassmaterials, such as laminates of glass and crystalline materials.Glass-based substrates according to one or more embodiments may beselected from soda-lime silicate glass, alkali-alumino silicate glass,alkali-containing borosilicate glass, alkali-containingaluminoborosilicate glass, and alkali-containing phosphosilicate.

A “base composition” is a chemical make-up of a substrate prior to anyion exchange (IOX) treatment. That is, the base composition is undopedby any ions from IOX.

It is noted that the terms “substantially” and “about” may be utilizedherein to represent the inherent degree of uncertainty that may beattributed to any quantitative comparison, value, measurement, or otherrepresentation. These terms are also utilized herein to represent thedegree by which a quantitative representation may vary from a statedreference without resulting in a change in the basic function of thesubject matter at issue. Thus, for example, a glass-based article thatis “substantially free of MgO” is one in which MgO is not actively addedor batched into the glass-based article, but may be present in verysmall amounts as a contaminant, such as amounts less than 0.01 mol %.

Unless otherwise specified, all compositions described herein areexpressed in terms of mole percent (mol %) on an oxide basis.

A “stress profile” is stress with respect to position of a glass-basedarticle or any portion thereof. A compressive stress region extends froma first surface to a depth of compression (DOC) of the article, wherethe article is under compressive stress. A central tension regionextends from the DOC to include the region where the article is undertensile stress.

As used herein, depth of compression (DOC) refers to the depth at whichthe stress within the glass-based article changes from compressive totensile stress. At the DOC, the stress crosses from a positive(compressive) stress to a negative (tensile) stress and thus exhibits astress value of zero. According to the convention normally used inmechanical arts, compression is expressed as a negative (<0) stress andtension is expressed as a positive (>0) stress. Throughout thisdescription, however, compressive stress (CS) is expressed as a positiveor absolute value—i.e., as recited herein, CS=|CS|. In addition, tensilestress is expressed herein as a negative (<0) stress or, in somesituations where the tensile stress is specifically identified, as anabsolute value. Central tension (CT) refers to tensile stress in acentral region or central tension region of the glass-based article.Maximum central tension (maximum CT or CT_(max)) occurs in the centraltension region, and often is located at 0.5·h, where h is the articlethickness. For the present disclosure of articles having first andsecond sections of different thicknesses, a first thickness (t₁) and asecond section having a second thickness (t₂), respectively, a firstmaximum central tension (CT₁) in the first section is nominally at0.5·t₁, and a second maximum central tension (CT₂) in the second sectionis nominally at 0.5·t₂. Reference to “nominally” at 0.5·h, at 0.5·t₁,and at 0.5·t₂ allows for variation from exact center of the location ofthe maximum tensile stress.

A “knee” of a stress profile is a depth of an article where the slope ofthe stress profile transitions from steep to gradual. The knee may referto a transition area over a span of depths where the slope is changing.

A non-zero alkali metal oxide concentration that varies along at least asubstantial portion of the article thickness (h), the first sectionthickness (t₁), or the second section thickness (t₂) indicates that astress has been generated in the article, first section, or secondsection, respectively, as a result of ion exchange. The variation inmetal oxide concentration may be referred to herein as a metal oxideconcentration gradient. The metal oxide that is non-zero inconcentration and varies along a portion of the thickness may bedescribed as generating a stress in the glass-based article. Theconcentration gradient or variation of one or more metal oxides iscreated by chemically strengthening a glass-based substrate in which aplurality of first metal ions in the glass-based substrate is exchangedwith a plurality of second metal ions.

Unless otherwise specified, CT and CS are expressed herein inmegaPascals (MPa), whereas thickness and DOC are expressed inmillimeters or microns (micrometers).

CS and DOC are measured using those means known in the art, such as byscattering polarimetry using a SCALP-5 measurement system fromGlasstress (Estonia). Other possible techniques for measuring CS and DOCinclude a surface stress meter (FSM) using commercially availableinstruments such as the FSM-6000, manufactured by Orihara IndustrialCo., Ltd. (Japan). Surface stress measurements rely upon the accuratemeasurement of the stress optical coefficient (SOC), which is related tothe birefringence of the glass. SOC in turn is measured according tothose methods known in the art, such a Procedure C (Glass Disc Method)described in ASTM standard C770-16, entitled “Standard Test Method forMeasurement of Glass Stress-Optical Coefficient,” the contents of whichare incorporated herein by reference in their entirety.

State-of-the-art ion exchange (IOX) of alkali-containing glass hasfocused on glass-based articles of uniform thickness. Glass-basedarticles, however, are now being designed with non-uniform thicknessesin areas away from the edges. One exemplary application is to have arecess in a glass-based cover to house a fingerprint sensor to replace atraditional through-hole or -slot for receipt of the fingerprint sensor.By housing the fingerprint sensor in strengthened glass, traditionalpolymeric fingerprint sensor covers are eliminated, allowing forimproved scratch resistance and better user experience because there areno protruding or slotted features on the cover glass. When substrateswith non-uniform thicknesses in areas away from the edges are chemicallystrengthened under state-of-the art IOX methods, thinner sections canhave higher central tension (CT) than the thicker sections. The higherCT in the thinner sections can be detrimental to the reliability of thefinal glass-based article and, in many cases, can make it frangible,which is a problem that was not previously recognized.

Glass-based articles disclosed herein are advantageous in that they havesections of different thicknesses in combination with a stress profilethat includes a first central tension in a first section having a firstthickness and a second central tension in a second section having asecond thickness, wherein the second thickness is less than the firstthickness, and the second central tension is less than the first centraltension. The glass-based articles are formed from substrates having oneor more alkali metals in a base composition, the substrates beingexposed to ion exchange such that the articles comprise one or moreion-exchanged metals. The one or more ion-exchanged metals may compriseone or more of: lithium, potassium, and sodium. Further ion-exchangedmetals may comprise one or more metals selected from the groupconsisting of: silver, copper, zinc, titanium, rubidium, and cesium.

Glass-based substrates may be strengthened by single-, dual-, ormulti-step ion exchange (IOX). Non-limiting examples of ion exchangeprocesses in which glass is immersed in multiple ion exchange baths,with washing and/or annealing steps between immersions, are described inU.S. Pat. No. 8,561,429, by Douglas C. Allan et al., issued on Oct. 22,2013, entitled “Glass with Compressive Surface for ConsumerApplications,” in which glass is strengthened by immersion in multiple,successive, ion exchange treatments in salt baths of differentconcentrations; and U.S. Pat. No. 8,312,739, by Christopher M. Lee etal., issued on Nov. 20, 2012, and entitled “Dual Stage Ion Exchange forChemical Strengthening of Glass,” in which glass is strengthened by ionexchange in a first bath diluted with an effluent ion, followed byimmersion in a second bath having a smaller concentration of theeffluent ion than the first bath. The contents of U.S. Pat. Nos.8,561,429 and 8,312,739 are incorporated herein by reference in theirentireties.

In the glass-based articles, there is an alkali metal oxide having anon-zero concentration that varies independently in both the firstsection along at least a portion of the t₁ and the second section alongat least a portion of the t₂. The stress profiles in each section aregenerated due to the non-zero concentration of the metal oxide(s) thatvaries along a portion of each thickness. In some embodiments, theconcentration of a metal oxide is non-zero and varies, both along athickness range from about 0·(t₁ or t₂) to about 0.3·(t₁ or t₂). In someembodiments, the concentration of the metal oxide is non-zero and variesalong a thickness range from about 0·(t₁ or t₂) to about 0.35·(t₁ ort₂), from about 0·(t₁ or t₂) to about 0.4·(t₁ or t₂), from about 0·(t₁or t₂) to about 0.45·(t₁ or t₂), from about 0·(t₁ or t₂) to about0.48·(t₁ or t₂), or from about 0·(t₁ or t₂) to about 0.50·(t₁ or t₂).The variation in concentration may be continuous along theabove-referenced thickness ranges. Variation in concentration mayinclude a change in metal oxide concentration of about at least about0.2 mol % along a thickness segment of about 100 micrometers. The changein metal oxide concentration may be at least about 0.3 mol %, at leastabout 0.4 mol %, or at least about 0.5 mol % along a thickness segmentof about 100 micrometers. This change may be measured by known methodsin the art including microprobe.

In some embodiments, the variation in concentration may be continuousalong thickness segments in the range from about 10 micrometers to about30 micrometers. In some embodiments, the concentration of the metaloxide decreases from the first surface of the first or second section toa point between the first surface and the second surface and increasesfrom the point to the second surface.

The concentration of metal oxide may include more than one metal oxide(e.g., a combination of Na₂O and K₂O). In some embodiments, where twometal oxides are utilized and where the radius of the ions differ fromone or another, the concentration of ions having a larger radius isgreater than the concentration of ions having a smaller radius atshallow depths, while at deeper depths, the concentration of ions havinga smaller radius is greater than the concentration of ions having largerradius. For example, where a single Na- and K-containing bath is used inthe ion exchange process, the concentration of K+ ions in theglass-based article is greater than the concentration of Na+ ions atshallower depths, while the concentration of Na+ is greater than theconcentration of K+ ions at deeper depths. This is due, in part, to thesize of the monovalent ions that are exchanged into the glass forsmaller monovalent ions. In such glass-based articles, the area at ornear the surface comprises a greater CS due to the greater amount oflarger ions (i.e., K+ ions) at or near the surface. Furthermore, theslope of the stress profile typically decreases with distance from thesurface due to the nature of the concentration profile achieved due tochemical diffusion from a fixed surface concentration.

In one or more embodiments, the metal oxide concentration gradientextends through a substantial portion of the thicknesses t₁ or t₂ or theentire thicknesses t₁ or t₂ of the sections. In some embodiments, theconcentration of the metal oxide may be about 0.5 mol % or greater(e.g., about 1 mol % or greater) along the entire thickness of the firstand/or second section, and is greatest at a first surface and/or asecond surface 0·(t₁ or t₂) and decreases substantially constantly to apoint between the first and second surfaces. At that point, theconcentration of the metal oxide is the least along the entire thicknesst₁ or t₂; however the concentration is also non-zero at that point. Inother words, the non-zero concentration of that particular metal oxideextends along a substantial portion of the thickness t₁ or t₂ (asdescribed herein) or the entire thickness t₁ or t₂. The totalconcentration of the particular metal oxide in the glass-based articlemay be in the range from about 1 mol % to about 20 mol %.

The concentration of the metal oxide may be determined from a baselineamount of the metal oxide in the glass-based substrate ion exchanged toform the glass-based article.

Turning to the figures, FIG. 1 illustrates a glass-based article 100having a non-uniform thickness away from edges. First section 102 has afirst thickness (t₁) and a first maximum central tension (CT₁). Line 114designates a midline of the article 100. Second section 104 has a secondthickness (t₂) and a second maximum central tension (CT₂). Generally,the difference between t₁ and t₂ is at least 100 microns. In one or moreembodiments, the t₁ is greater than the t₂ by at least 100 microns. Thet₂ may be in the range of 0.05·t₁ to 0.96·t₁. In one or moreembodiments, the t₂ is reduced by about 20% relative to t₁, or by about30%, about 40%, about 50%, about 60%, about 70%, about 80%, about 90%,about 95%, and all values and subranges therebetween. The t₁ may be inthe range of 0.3 mm to 2.5 mm, and all values and subrangestherebetween; and the t₂ may be in the range of 0.025 mm to 2.4 mm, andall values and subranges therebetween. CT₂ is less than the CT₁, whichis advantageous for ensuring the second section is not frangible despitehaving been ion exchanged under the same conditions as the firstsection. While the figures depict a single section having a thicknessdifferent from the rest of the article, it is noted that there may bemultiple sections or pockets of different depths in the same article.

In this embodiment, the second section 104 is off-set from all edges106, 108, 110, and 112 of the article 100. That is, second section 104does not intersect any of the edges 106, 108, 110, 112.

FIG. 2 illustrates the second section 104 being defined by sides 116,118, 120, and 122. In this embodiment, the second section 104 is a thinpocket designed to accommodate a fingerprint sensor or the like. Line124 designates a centerline of the second section 104. FIG. 3illustrates a cross-section of the article 100 along line 124 of FIG. 2. Sides 116, 118, 120, and 122 provide a transition from a body 105 ofthe second section 104 to the first section 102. In some embodiments,the article has a size of 141.4 millimeters by 68.4 millimeters and thefirst section is 0.6 millimeters thick. In some embodiments, the pockethas a size of 5.6 millimeters by 12.3 millimeters and the second sectionis 0.3 millimeters thick.

FIG. 4A illustrates a cross-section of the article 100 along midline 114of FIG. 1 and the location of second section 104. FIG. 4B illustrates aclose-up of the cross-section of the second section 104 having sides 120and 122 which transition to the first section 102.

The glass-based articles disclosed herein may be incorporated intoanother article such as an article with a display (or display articles)and/or a housing (e.g., consumer electronics, including mobile phones,tablets, computers, navigation systems, and the like), architecturalarticles, transportation articles (e.g., automobiles, trains, aircraft,sea-craft, etc.), appliance articles, or any article that requires sometransparency, scratch-resistance, abrasion resistance or a combinationthereof. An exemplary article incorporating any of the strengthenedarticles disclosed herein is shown in FIGS. 5A and 5B. Specifically,FIGS. 5A and 5B show a consumer electronic device 300 including ahousing 302 having front 304, back 306, and side surfaces 308;electrical components (not shown) that are at least partially inside orentirely within the housing and including at least a controller, amemory, and a display 310 at or adjacent to the front surface of thehousing; and a cover plate 312 at or over the front surface of thehousing such that it is over the display. In some embodiments, the atleast a portion of cover plate 312 may include any of the strengthenedarticles disclosed herein. In some embodiments, at least a portion ofthe housing 302 may include any of the strengthened articles disclosedherein.

Glass-based substrates may be provided using a variety of differentprocesses. For example, exemplary glass-based substrate forming methodsinclude float glass processes and down-draw processes such as fusiondraw and slot draw. A glass-based substrate prepared by floating moltenglass on a bed of molten metal, typically tin to produce a float glasscharacterized by smooth surfaces and uniform thickness. In an exampleprocess, molten glass that is fed onto the surface of the molten tin bedforms a floating glass ribbon. As the glass ribbon flows along the tinbath, the temperature is gradually decreased until the glass ribbonsolidifies into a solid glass-based substrate that can be lifted fromthe tin onto rollers. Once off the bath, the glass-based substrate canbe cooled further, annealed to reduce internal stress, and optionallypolished.

Down-draw processes produce glass-based substrates having a uniformthickness that possess relatively pristine surfaces. Because the averageflexural strength of the glass-based substrate is controlled by theamount and size of surface flaws, a pristine surface has a higherinitial strength. When this high strength glass-based substrate is thenfurther strengthened (e.g., chemically), the resultant strength can behigher than that of a glass-based substrate with a surface that has beenlapped and polished. Down-drawn glass-based substrates may be drawn to athickness of less than about 2 mm. In addition, down drawn glass-basedsubstrates have a very flat, smooth surface that can be used in itsfinal application without costly grinding and polishing.

The fusion draw process, for example, uses a drawing tank that has achannel for accepting molten glass raw material. The channel has weirsthat are open at the top along the length of the channel on both sidesof the channel. When the channel fills with molten material, the moltenglass overflows the weirs. Due to gravity, the molten glass flows downthe outside surfaces of the drawing tank as two flowing glass films.These outside surfaces of the drawing tank extend down and inwardly sothat they join at an edge below the drawing tank. The two flowing glassfilms join at this edge to fuse and form a single flowing glass-basedsubstrate. The fusion draw method offers the advantage that, because thetwo glass films flowing over the channel fuse together, neither of theoutside surfaces of the resulting glass-based substrate comes in contactwith any part of the apparatus. Thus, the surface properties of thefusion drawn glass-based substrate are not affected by such contact.

The slot draw process is distinct from the fusion draw method. In slotdraw processes, the molten raw material glass is provided to a drawingtank. The bottom of the drawing tank has an open slot with a nozzle thatextends the length of the slot. The molten glass flows through theslot/nozzle and is drawn downward as a continuous substrate and into anannealing region.

Exemplary base compositions of substrates may comprise but are notlimited to: a soda-lime silicate, an alkali-alumino silicate, analkali-containing borosilicate, an alkali-containingaluminoborosilicate, or an alkali-containing phosphosilicate.Glass-based substrates may include a lithium-containing aluminosilicate.

Examples of glasses that may be used as substrates may includealkali-alumino silicate glass compositions or alkali-containingaluminoborosilicate glass compositions, though other glass compositionsare contemplated. Such glass compositions may be characterized as ionexchangeable. As used herein, “ion exchangeable” means that a substratecomprising the composition is capable of exchanging cations located ator near the surface of the substrate with cations of the same valencethat are either larger or smaller in size.

In an embodiment, the base glass composition comprises a soda limesilicate glass. In and embodiment, the soda lime silicate glasscomposition is, on an oxide basis: 73.5 wt. % SiO₂, 1.7 wt. % Al₂O₃,12.28 wt.-% Na₂O, 0.24 wt. % K₂O, 4.5 wt. % MgO, 7.45 wt. % CaO, 0.017wt. % ZrO₂, 0.032 wt. % TiO₂, 0.002 wt. % SnO₂, 0.014 wt. % SrO, 0.093wt. % Fe₂O₃, 0.001 wt. % HfO₂, 0.028 wt. % Cl oxide(s), and 0.203 wt. %SO₃.

In a particular embodiment, an alkali-alumino silicate glass compositionsuitable for the substrates comprises alumina, at least one alkali metaland, in some embodiments, greater than 50 mol. % SiO₂, in otherembodiments at least 58 mol. % SiO₂, and in still other embodiments atleast 60 mol. % SiO₂, wherein the ratio ((Al₂O₃+B₂O₃)/Σmodifiers)>1,where in the ratio the components are expressed in mol. % and themodifiers are alkali metal oxides. This glass composition, in particularembodiments, comprises: 58-72 mol. % SiO₂; 9-17 mol. % Al₂O₃; 2-12 mol.% B₂O₃; 8-16 mol. % Na₂O; and 0-4 mol. % K₂O, wherein the ratio((Al₂O₃+B₂O₃)/Σmodifiers)>1.

In still another embodiment, the substrates may include an alkalialuminosilicate glass composition comprising: 64-68 mol. % SiO₂; 12-16mol. % Na₂O; 8-12 mol. % Al₂O₃; 0-3 mol. % B₂O₃; 2-5 mol. % K₂O; 4-6mol. % MgO; and 0-5 mol. % CaO, wherein: 66 mol. %≤(SiO₂+B₂O₃+CaO)≤69mol. %; (NaO+K₂O+B₂O₃+MgO+CaO+SrO)>10 mol. %; 5 mol. %<(MgO+CaO+SrO)≤8mol. %; (Na₂O+B₂O₃)<Al₂O₃<2 mol. %; 2 mol. %<Na₂O<Al₂O₃<6 mol. %; and 4mol. %<(Na₂O+K₂O)<Al₂O₃≤10 mol. %.

In an alternative embodiment, the substrates may comprise an alkalialuminosilicate glass. In an embodiment, the alkali aluminosilicateglass has a composition comprising: 2 mol. % or more of Al₂O₃ and/orZrO₂, or 4 mol % or more of Al₂O₃ and/or ZrO₂.

In another embodiment, the substrates may comprise a lithium-containingalkali aluminosilicate glass. In an embodiment, the lithium-containingalkali aluminosilicate glass has a composition including, in mol %, SiO₂in an amount in the range from about 60% to about 75%, Al₂O₃ in anamount in the range from about 12% to about 20%, B₂O₃ in an amount inthe range from about 0% to about 5%, Li₂O in an amount in the range fromabout 2% to about 8%, Na₂O in an amount greater than about 4%, MgO in anamount in the range from about 0% to about 5%, ZnO in an amount in therange from about 0% to about 3%, CaO in an amount in the range fromabout 0% to about 5%, and P₂O₅ in a non-zero amount; wherein the glasssubstrate is ion-exchangeable and is amorphous, wherein the total amountof Al₂O₃ and Na₂O in the composition is greater than about 15 mol %.

Chemical strengthening of glass substrates having base compositions isdone by placing the ion-exchangeable glass substrates in a molten bathcontaining cations (K+, Na+, Ag+, etc) that diffuse into the glass whilethe smaller alkali ions (Na+, Li+) of the glass diffuse out into themolten bath. The replacement of the smaller cations by larger onescreates compressive stresses near the top surface of glass. Tensilestresses are generated in the interior of the glass to balance thenear-surface compressive stresses. For a flat piece of glass of uniformthickness, stress (σ(z)) can be calculated from the concentrationprofile according to equation (I):

$\begin{matrix}{{\sigma(z)} = {{\frac{BE}{1 - v}( {C_{avg} - {C(z)}} )} = {\frac{BE}{1 - v}{( {{\frac{1}{h}{\int\limits_{0}^{h}{{C(z)}{dz}}}} - {C(z)}} ).}}}} & (I)\end{matrix}$

where C(z) is the concentration of the large cations at z, C_(avg) isthe average concentration of the large cations in the article, h is theglass thickness, B is the network dilation coefficient, E is the Young'smodulus, v is the Poisson's ratio, and z is the co-ordinate in thethickness direction with values 0 and h at the surfaces of the article.Concentration of the larger ions is typically maximum at the surface andminimum at the mid-thickness. Near the surface, where C(z)>C_(avg),stresses are compressive. When C(z)=C_(avg), stress becomes zero, andthis depth is referred to as the depth of compression (DOC). At greaterdepths, where C(z)<C_(avg), stresses are tensile, and generally reach amaximum value at the mid-thickness of the article. This maximum value oftensile stress is referred to as the maximum central tension.

Glass-based substrates may be exposed to a first bath comprising alkalimetal ions for a first duration, and subsequently to a second bathcomprising alkali metal ions for a second duration. In a detailedembodiment, the glass-based substrate is a lithium-containingaluminosilicate and the bath comprises ions of potassium and sodium.

Higher compressive stresses (CS) are desired for better scratchresistance and drop performance. Higher DOC also improves dropperformance, and is therefore preferred as well. However, higher CS andDOC lead to higher CT, which is undesirable for crack propagation and,if too high, can lead to frangibility of the sample.

FIG. 6 is a graph of three parameters: compressive stress (CS), maximumcentral tension (CT), and depth of compression (DOC) as a function ofscaled diffusion distance, sqrt(4Dt)/h, with DOC being represented as afraction of total thickness, h. D is the diffusivity and t is time.Trends are for a 1-step, 3-ion diffusion exchange where one exchangepair (Li—Na) provides the parabolic stress profile, and a secondexchange pair (Na—K) provides the spike. When represented in this way,curves for glass articles of different thicknesses overlap. The preciseshape of the curve depends on concentration dependence of diffusivity,pairs of ions exchanged (e.g. K+ for Na⁺, Na⁺ for Li⁺, etc), and numberof IOX steps done at different bath compositions and/or temperatures.For example, addition of a short-depth high-slope high CS spike to analready IOX′d glass article typically reduces the DOC. The scale of theCS and CT curves in FIG. 6 , on the other hand, are determined by theterm BEΔC/(1−v), where ΔC is the difference between the surfaceconcentration and the concentration of the base substrate composition ofthe large cations. B is the network dilation coefficient and isdependent on the ion-exchange pairs, and E is the Young's modulus and isfixed for each glass composition. AC can be adjusted by changing thecomposition and temperature of the IOX bath. FIG. 6 shows the followingtrends.

Both DOC and CT first increase with the term sqrt(4Dt)/h, reach amaximum, and then decrease upon further ion-exchange. For a case of1-step 2-ion exchange (not shown), the DOC vs sqrt(4Dt)/h would reach astable value (˜0.22). The decrease in DOC beyond the peak (in FIG. 6 )is due to the effect of the spike. Compressive stress decreasesmonotonically with sqrt(4Dt)/h.

With respect to DOC, initially, as more and more ions diffuse into theglass, the location where C(z)=C_(avg) gets pushed further towards thecenter. That is, DOC increases with IOX time. For 3-ion IOX, where onepair of ions (e.g. Li—Na) creates the deep or parabolic portion of thestress profile and another pair (e.g. Na—K) creates the spike as shownin FIG. 6 , the DOC first reaches a plateau and then starts decreasing.Note that for infinite IOX time, concentration would be uniformeverywhere. DOC would under such conditions eventually reach zero evenfor the 1 step 2-ion exchange.

As to CT, initially, an increase in IOX time leads to an increase inC_(avg) without any increase in concentration at mid-thickness,C(z=h/2). During this period, CT increases according to Equation I.However, as the ions start reaching the center, the rate of increase inC_(avg) is exceeded by the rate of increase in C(z=h/2). From this pointonwards, CT starts decreasing. Thus, DOC and CT show similar trends(increasing at first, then decreasing, with IOX time), but the peaks forDOC and CT are reached at different IOX times.

Regarding CS, with an increase in IOX time, the average concentration inthe glass steadily increases with little corresponding change in surfaceconcentration. Therefore, surface CS decreases gradually with anincrease in IOX time.

FIG. 7 is a graph of scaled concentration versus normalized positionfrom the surface, for sqrt(4Dt)/h values of 0.075, 0.15, 0.25, and 0.40.Dashed lines show the average concentration (scaled) values for thecurve of the corresponding sqrt(4Dt)/h value. Dotted lines represent theparabolic fit curves for sqrt(4Dt)/h=0.25 and 0.40. Intersection ofsolid curves with dashed lines represents the DOC. DOC increases withIOX time.

FIG. 8 is a graph of stress versus normalized position from the surface,for values of sqrt(4Dt)/h corresponding to those of FIG. 7 . Parabolicfit curves for sqrt(4Dt)/h=0.25, 0.40 are also shown. Forsqrt(4Dt/h<0.25, ions from the surface have not reached the center ofthe glass. Up to this point, the concentration and stress profilesresemble a single error function (erfc) profile resulting from thesolution of Fick's law of diffusion for short diffusion times. Forsqrt(4Dt/h<0.25, the solution of Fick's law involves addition ofmultiple erfc terms, and the resulting profile can be approximated by aparabolic equation y=ax{circumflex over ( )}2+bx+c.

The graphs of FIGS. 7-8 are representative of 1-step ion-exchangeprocesses with only one pair of exchanging species (Na+ for Li+, K+ forNa+, etc). However, these concepts can be applied to multi-pair and/ormulti-step ion-exchange processes as well. A typical case may be of onepair of ion-exchange (e.g. Na+ with Li+) or first step accounting forthe deep portion of ion-exchange and another pair (K+ with Na+)accounting for the steep surface spike.

When a glass article of non-uniform thickness (e.g., FIGS. 1-4 ) isIOX'd, all surfaces are exposed to substantially the same surfaceconcentration at the same temperature. Thus, the values of parametersCS, DOC, and CT can be determined from the same curve. As the value ofsqrt(4Dt)/h is higher for thinner sections of the glass, the CS, CT, andDOC values for the thinner section will be shifted towards the right(relative to thicker sections) of the curve in FIG. 6 . Taking, forexample, a first thickness of 0.6 mm and a second thickness of 0.3 mm,the sqrt(4Dt)/h value for the thin 0.3 mm section is twice the value forthe thick 0.6 mm section. In this example, as the bulk of the article is0.6 mm thick, it is desirable to have DOC at or close to peak of thecurve. As peak CT is located to the left of peak DOC (FIG. 6 ), CT iseither close to or already on the declining side of the curve.Therefore, for the 0.3 mm thick areas, CT value will be much lower thanthe peak. The same case holds for DOC, which is undesirable. However,for articles such as this, where the thinner areas are a small fractionof the thicker areas, having CT below the frangibility limit is moreimportant than a slightly reduced DOC.

For designs where the area of thin sections is a significant fraction ofthe total area, DOC may be increased, while still maintaining CT belowfrangibility limits, by shifting to lower IOX times for a particularglass composition. This may decrease the DOC and/or CT in the thickersections.

DOC in the thick sections may be >0.15 h, and is preferably >0.18 h. Forthe example of FIG. 6 , this can be achieved by having0.18<sqrt(4Dt/h₁)<0.67, and preferably 0.25<sqrt(4Dt/h₁)<0.51, where h₁is the thickness of the thick section, and D is the diffusivity. DOC inthe thin sections may be >0.075 h₂, and is preferably greater than 0.1h₂, where h₂ is the thickness of the thin section. For the example inFIG. 6 , this can be achieved by having 0.07<sqrt(4Dt/h₂)<0.85. Inanother embodiment, the DOC in the thinnest section is >10 microns, andis preferably >20 microns.

For a particular IOX bath composition and temperature, IOX times can becalculated based on diffusivities of larger ions diffusing into theglass (K or Na) and maximum and minimum thicknesses of the article. DOCat the thickest section will determine the minimum IOX time and the DOCat thinnest section will determine the maximum IOX time, e.g. 0.01561h₁/D<t<0.18 h₂/D.

The surface CS in the thickest and thinnest sections may be >450 MPa,and preferably >650 MPa. CS can be adjusted by changing theconcentration and temperature of the ion-exchange bath.

Maximum CT values in the thin section are below the frangibility limit.

Articles may have a high-slope (>10 MPa/um) region of the compressivestress profile near the surface extending over a depth of about 2-30microns or about 5-20 um. A peak compressive stress of >450 MPa, andpreferably >650 MPa, may be present at the surface. This region may bereferred to as the spike.

A deep, low slope (<2 MPa/um) region of the compressive stress profilemay extend from a depth of ˜20-30 um to the center of the article. Thisregion is characterized by a parabolic (stress=az²+bz+c) ornear-parabolic shape. The actual profile in this region may deviatesomewhat due to various factors, such as concentration dependentdiffusivity.

To form substrates having non-uniform thicknesses, a variety ofprocesses may be used. A substrate of substantially uniform thicknessmay be obtained, where the thickness is the desired thickness of thefirst section. A second section of a thinner thickness may be formed inthe first section of a thicker thickness by removal of a portion of thefirst section. Removal may be effected by mechanical treatment, such asmachining, or by chemical treatment, such as etching, or by combinationsof mechanical and chemical treatments. Substrates having non-uniformthicknesses may be formed by using a mold with a thin section designedtherein. In some embodiments, the mold may be selected to produce thedesired substrate profile with sections of difference thicknesses. Insome embodiments, the molded substrate may in turn be subjected tofurther processing, such as machining, etching, or combinations thereofto form sections of different thicknesses.

The substrates of non-uniform thicknesses are then ion exchanged to formstrengthened glass-based articles. The ion exchange conditions areselected to achieve a stress profile including a desired depth ofcompression (DOC) in the thick section while maintaining a centraltension (CT) in the thin section to ensure the thin section is notfrangible. Upon ion exchange of the substrate with non-uniformthickness, a glass-based article having sections of differentthicknesses comprising a base composition and one or more ion-exchangedmetals is formed.

Frangible behavior may be characterized by at least one of: breaking ofthe strengthened glass article (e.g., a plate or sheet) into multiplesmall pieces (e.g., ≤1 mm); the number of fragments formed per unit areaof the glass article; multiple crack branching from an initial crack inthe glass article; violent ejection of at least one fragment to aspecified distance (e.g., about 5 cm, or about 2 inches) from itsoriginal location; and combinations of any of the foregoing breaking(size and density), cracking, and ejecting behaviors. As used herein,the terms “frangible behavior” and “frangibility” refer to those modesof violent or energetic fragmentation of a strengthened glass articleabsent any external restraints, such as coatings, adhesive layers, orthe like. While coatings, adhesive layers, and the like may be used inconjunction with the strengthened glass articles described herein, suchexternal restraints are not used in determining the frangibility orfrangible behavior of the glass articles.

In some embodiments, a first depth of compression (DOC₁) in the firstsection is located at 0.15·t₁ or deeper. The DOC₁ may be in the range of0.15·t₁ to 0.23·t₁, and all values and subranges therebetween.

In some embodiments, a second depth of compression (DOC₂) in the secondsection, the DOC₂ being located at 0.075·t₂ or deeper. The DOC₂ may inthe range of 0.075·t₂ to 0.15·t₂, and all values and subrangestherebetween.

In some embodiments, the glass-based articles may have a surfacecompressive stress in the first section (CS₁) of 450 MPa or more, and asurface compressive stress in the second section (CS₂) of 450 MPa ormore. CS₁ and CS₂ may independently be in the range of 450 MPa to 1.2GPa, 700 MPa to 950 MPa, or about 800 MPa, and all values and subrangestherebetween.

In some embodiments, the stress profile of the first section furthercomprises a compressive stress region extending from a first sectionsurface or below to a knee in the range of about 2 to about 30micrometers, wherein all points of the compressive stress region betweenthe first section surface and the knee comprise a tangent having a valuethat is 10 MPa/micrometer or greater. The tangent value may be in therange of about 10 to about 500 MPa/micrometer, and all values andsubranges therebetween.

In some embodiments, the stress profile in the first region furthercomprises an internal stress region extending from the knee thatdecreases such that all points of the internal stress region extendingfrom the knee to a center of the article comprise a tangent having avalue that is between about 0 and about 5 MPa/micrometer, and all valuesand subranges therebetween.

EXAMPLES

Various embodiments will be further clarified by the following examples.In the Examples, prior to strengthening, the Examples are referred to as“substrates”. After being subjected to strengthening, the Examples arereferred to as “articles” or “glass-based articles”.

The following examples were designed and stress profiles were generatedusing a two-dimensional (2D) plane strain ion exchange (IOX) model,which is based on finite element modeling.

Example 1

A glass-based article formed from an alkali-alumino silicate glasssubstrate by ion exchange was modeled. The substrate had a basecomposition of: 63.60 mol % SiO₂, 15.67 mol % Al₂O₃, 10.81 mol % Na₂O,6.24 mol % Li₂O, 1.16 mol % ZnO, 0.04 mol % SnO₂, and 2.48 mol % P₂O₅.The IOX included two steps. Step 1 was in a bath at a 380° C. bathtemperature for 1 hour and 50 minutes, where the bath contained 38 wt. %Na and 62 wt. % K. Step 2 was in a bath at a temperature of 380° C. for33 minutes, where the bath contained 9 wt. % Na and 91 wt. % K. Theion-exchanged metals therefore comprised K and Na. The article had afirst section having a thickness of 0.6 millimeters and a second sectionhaving a thickness of 0.3 millimeters.

Comparative Example A

A glass-based article formed from an alkali-alumino silicate glasssubstrate by ion exchange was modeled. The substrate was produced inaccordance with U.S. Pat. No. 9,156,724, which is incorporated herein byreference. The substrate had a base composition of: 57.43 mol % SiO₂,16.10 mol % Al₂O₃, 17.05 mol % 2.81 mol % MgO, 0.003 mol % TiO₂, 6.54mol % P₂O₅, and 0.07 mol % SnO₂. The simulated IOX included two steps.Step 1 was in a bath at a 450° C. bath temperature for 8 hours and 30minutes, where the bath contained 51 wt. % Na and 49 wt. % K. Step 2 wasin a bath at a 390° C. bath temperature for 14 minutes, where the bathcontained 0.5 wt. % Na and 99.5 wt. % K. The ion-exchanged metalstherefore comprised K and Na. The article had a first section having athickness of 0.6 millimeters and a second section having a thickness of0.3 millimeters.

Example 2

Stress profiles for each section (thick and thin) of Example 1 andComparative Example A are provided in FIGS. 9-11 in accordance with the2D plane strain model. Stresses in MPa versus absolute position(microns) from the surface of the article are provided in FIG. 9 , andstresses versus normalized position (z/h) are provided in FIGS. 10 and11 . FIG. 11 is an enlarged version of FIG. 10 to the center point (0.5h) of the article. Table 1 summarizes compressive stress (CS), maximumcentral tension (CT_(max)), and depth of compression (DOC) for eachsection of each example. The knee depth of each section of the samplesis identified along with the compressive stress at the knee (CSk). Slopein a surface compressive stress region may be determined by a best fitline through the surface to the knee. Slope in an internal stress regionmay be determined by a best fit line from the knee to the center.

TABLE 1 Maximum Central Absolute Compressive Tension Slope Stress (CS)(CT_(max)) DOC (MPa/ (MPa) (MPa) (microns) micron) Example 1 1st Section(0.6 mm) 800 −63 113 Compressive Surface (0 microns) for CS (0.18 h)Stress Region Center (337 microns) for CT 73.0 1st Section 111 — —Internal Stress Knee (9.42 microns) Region 1.9 2nd Section (0.3 mm) 745−40 31 Compressive Surface (0 microns) for CS (0.10 h) Stress RegionCenter (175 microns) for CT 57.8 2nd Section 22.7 — — Internal StressKnee (12.5 microns) Region 0.4 Comparative 1st Section (0.6 mm) 828 −4973 Compressive Example A Surface (0 microns) for CS (0.12 h) RegionCenter (316 microns) for CT 63.6 1st Section 229 — — Internal Knee (9.42microns) Region 0.9 2nd Section (0.3 mm) 794 −93 49.5 CompressiveSurface (0 microns) for CS (0.16 h) Region Center (156 microns) for CT51.6 2nd Section 150 — — Internal Knee (12.5 microns) Region 1.7

With respect to Example 1, CT in the thick section was −63 MPa, and CTin the thin section was −40 MPa. Thus, the CT is reduced in the thinsection versus the thick section for the same IOX treatment. Incontrast, for Comparative Example A, CT in the thick section was −49MPa, and CT in the thin section was −93 MPa, and thus, the CT isincreased in the thin section versus the thick section for the same IOXtreatment. The thin section of Comparative Example A is frangible basedon its maximum CT. To make the thin section of Comparative Example Anon-frangible, the degree of IOX would need to be reduced in order toreduce maximum CT of the thin section, with the undesirable consequenceof lower DOC in this thick section.

While the foregoing is directed to various embodiments, other andfurther embodiments of the disclosure may be devised without departingfrom the basic scope thereof, and the scope thereof is determined by theclaims that follow.

What is claimed is:
 1. A method of manufacturing a glass-based articlecomprising: exposing a glass-based substrate to a bath comprising alkalimetal ions to ion-exchange the glass-based substrate for a period oftime (t), the glass-based substrate comprising first section having afirst thickness (h₁) and a second section having a second thickness(h₂), the exposing forms the glass-based article comprising: an alkalimetal oxide having a first non-zero concentration that varies in thefirst section from a first section surface into at least a portion ofthe first thickness, and the first section having a first stressprofile; and a second non-zero concentration that varies in the secondsection from a second section surface into at least a portion of thesecond thickness, and the second section having a second stress profile,wherein the glass-based substrate comprises a diffusivity D, and 0.01561h₁/D<t<0.18 h₂/D.
 2. The method of claim 1, wherein0.07<sqrt(4Dt/h₂)<0.85.
 3. The method of claim 1, wherein0.18<sqrt(4Dt/h₁)<0.67.
 4. The method of claim 3, wherein0.25<sqrt(4Dt/h₁)<0.51.
 5. The method of claim 1, wherein the firststress profile comprises a first central tension region comprising afirst maximum central tension (CT₁), the second stress profile comprisesa second central tension region comprising a second maximum centraltension (CT₂), and |CT₂| is less than |CT₁|.
 6. The method of claim 1,wherein the first stress profile comprises a first depth of compression(DOC₁), the second stress profile comprises a second depth ofcompression (DOC₂), DOC₁>0.15·h₁, and DOC₂ is in a range from 0.075·h₂to 0.15·h₂.
 7. The method of claim 1, wherein the first stress profilecomprises a first surface compressive stress (CS₁) in a firstcompressive stress region of 450 MPa or more, and the second stressprofile comprises a second surface compressive stress (CS₂) in a secondcompressive stress region of 450 MPa or more.
 8. The method of claim 1,wherein a portion of the first stress profile extends from the firstsection surface to a knee, the knee is located at a depth from the firstsection surface in a range from about 2 micrometers to about 30micrometers, and all points of the first stress profile located betweenthe first section surface and the knee comprise a tangent having a valuethat is 10 MPa/micrometer or greater.
 9. The method of claim 8, whereina portion of the first stress profile extends from the knee to a firstdepth of compression (DOC₁), wherein all points of the first stressprofile located between the knee and DOC₁ comprise a tangent having avalue from 0 MPa/micrometer to about 2 MPa/micrometer.
 10. The method ofclaim 1, wherein the glass-based substrate comprises a soda-limesilicate, an alkali-aluminosilicate, an alkali-containing borosilicate,an alkali-containing aluminoborosilicate, or an alkali-containingphosphosilicate.
 11. The method of claim 10, wherein the glass-basedsubstrate is a lithium-containing aluminosilicate.
 12. The method ofclaim 11, wherein the alkali metal ions include potassium.
 13. Themethod of claim 1, wherein h₁ is in a range from 0.3 mm to 2.5 mm, andh₂ is in a range from 0.025 mm to 2.4 mm.
 14. The method of claim 1,wherein h₂ is in a range from 0.05·h₁ to 0.96·h₁.
 15. The method ofclaim 1, wherein h₂ is less than h₁ by at least 100 microns.
 16. Themethod of claim 1, wherein the alkali metal ions comprise one or morepotassium, sodium, or combinations thereof.
 17. The method of claim 1,The glass-based article of claim 1, wherein the alkali metal ionscomprise are selected from a group consisting of: silver, copper, zinc,titanium, rubidium, cesium, and combinations thereof.
 18. The method ofclaim 1, wherein the alkali metal oxide is selected from a groupconsisting of: silver, copper, zinc, titanium, rubidium, and cesium. 19.The method of claim 1, wherein the alkali metal oxide comprisespotassium.
 20. The method of claim 1, wherein the glass-based substratecomprises: from 64 mol % to 68 mol % SiO₂; from 12 mol % to 16 mol %Na₂O; from 8 mol % to 12 mol % Al₂O₃; from 0 mol % to 3 mol % B₂O₃; from2 mol % to 5 mol % K₂O; from 4 mol % to 6 mol % MgO; and from 0 mol % to5 mol % CaO, wherein: 66 mol %<(SiO₂+B₂O₃+CaO)≤69 mol %;(Na₂O+K₂O+B₂O₃+MgO+CaO+SrO)>10 mol %; 5 mol %<(MgO+CaO+SrO)≤8 mol %;(Na₂O+B₂O₃)<Al₂O₃<2 mol %; 2 mol %<Na₂O<Al₂O₃<6 mol %; and 4 mol%<(Na₂O+K₂O)<Al₂O₃≤10 mol %.